Method and system for fluid flow rate measurement

ABSTRACT

A fluid flow meter system for monitoring fluid flow through a lumen includes a first ultrasonic transducer configured to transmit one or more versions of a transmit (TX) signal through a fluid flowing within the lumen, and a second ultrasonic transducer configured to receive one or more respective receive (RX) signals. The fluid flow meter system includes an analog-to-digital converter (ADC) configured to sample, at a first frequency, the one or more RX ultrasonic signals and a processor configured to generate a fine resolution signal based on the one or more RX ultrasonic signals. The fine resolution signal is associated with a second sampling rate higher than the first sampling rate. The processor is also configured to compute a cross-correlation signal indicative of cross-correlation between the fine resolution signal and a waveform and determine an estimated fluid flow parameter based on the computed cross-correlation signal.

RELATED APPLICATION

This application is a continuation of U.S. application Ser. No. 15/527,691, entitled “METHOD AND SYSTEM FOR FLUID FLOW RATE MEASUREMENT” and filed on May 13, 2016, which is a U.S. National Phase under 35 U.S.C. § 365(a) of International Application No. PCT/US2016/032401, filed May 13, 2016, which claims priority to U.S. patent application Ser. No. 14/741,124, entitled “METHOD AND SYSTEM FOR FLUID FLOW RATE MEASUREMENT” and filed on Jun. 16, 2015, which claims priority to U.S. Provisional Application No. 62/162,568, entitled “METHOD AND SYSTEM FOR FLUID FLOW RATE MEASUREMENT” and filed on May 15, 2015. The entire contents of the foregoing applications are hereby incorporated herein by reference.

BACKGROUND

Monitoring fluid flow rate in fluid distribution system can allow for pump efficiency (such as in systems employing pumps), leak detection or remote monitoring of fluid distribution systems. In water distribution systems, monitoring water flow rate can help monitoring water usage and detecting water leaks. When water leaks are detected at an early stage, substantial damage to buildings can be avoided. In natural gas distribution system, reliable leak detection can help avoid dangerous fires and/or explosions.

SUMMARY

According to at least one aspect, a fluid flow meter system for monitoring fluid flow through a lumen includes an ultrasonic sensor. The ultrasonic sensor can include a first ultrasonic transducer configured to transmit one or more versions of a transmit (TX) ultrasonic signal through a fluid flowing within the lumen, and a second ultrasonic transducer configured to receive one or more receive (RX) ultrasonic signals corresponding to the one or more transmitted versions of the TX ultrasonic signal. The fluid flow meter system includes an analog-to-digital converter (ADC) configured to sample, at a first frequency, the one or more RX ultrasonic signals received by the second transducer. The fluid flow meter system also includes a processor configured to generate a fine resolution signal based on the one or more RX ultrasonic signals. The fine resolution signal is associated with a second sampling rate higher than the first sampling rate. The processor is also configured to compute a cross-correlation signal indicative of cross-correlation between the fine resolution signal and a waveform and determine an estimated fluid flow rate (or fluid flow velocity) of the fluid based on the computed cross-correlation signal.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a diagram illustrating a flow meter system mounted on a pipe.

FIG. 2 is a flow diagram illustrating a method for estimating fluid flow rate or fluid flow velocity.

FIG. 3 is a diagram illustrating different implementations of copies or versions of a transmit (TX) signal for transmission within a given time period.

FIGS. 4A-4C show simulation results illustrating behavior of differential propagation times between downstream and upstream TX signals in a zero-flow fluid with and without jitter delays.

FIG. 5 is a diagram illustrating a process of interleaving samples from multiple received RX signals to generate a respective higher resolution interleaved signal.

FIG. 6 is a diagram illustrating a process of up-sampling a digital signal associated with one or more ADC-sampled RX signals to generate a respective higher resolution up-sampled RX signal.

FIG. 7 shows experimental results for measured differential propagation times using up-sampled RX signals.

FIG. 8A shows a block diagram illustrating a process 800 of estimating a time shift between a reference waveform and a fine resolution RX signal based on partial cross-correlation signal(s).

FIG. 8B shows an illustration of the first and second cross correlation signals.

FIG. 8C shows a cross-correlation plot and a state machine diagram illustrating a process for determining a cross-correlation peak value associated with a respective time window.

FIG. 8D is a diagram illustrating a ternary search for locating a feature value (such as local maximum or local minimum) within a time window.

FIG. 9 shows a block diagram illustrating another method for estimating fluid flow rate (or fluid flow velocity) based on recorded ultrasonic signals.

DETAILED DESCRIPTION

Systems and devices described in the current disclosure allow for accurate and cost effective estimation of flow rate (or flow velocity/speed) for a fluid flowing through a lumen such as a pipe. In particular, an ultrasonic fluid flow meter can include ultrasonic transducers capable of transmitting/receiving ultrasonic signals to propagate through the fluid flowing in the lumen. The ultrasonic flow meter can estimate the fluid flow rate (or fluid flow velocity) based on measured or estimated propagation characteristics of the ultrasonic signal within the fluid. The ultrasonic signal propagation speed (or propagation time) can vary depending on the type of fluid, fluid flow direction and speed with respect to signal propagation direction, fluid temperature, or other fluid parameters that can affect fluid density or fluid compressibility.

An ultrasonic signal propagating in the same direction as a fluid flow (i.e., downstream) propagates faster than another ultrasonic signal propagating opposite to fluid flow direction (i.e. upstream) or faster than an ultrasonic signal propagating in non-moving fluid. Fluid flow speed (or fluid flow rate) can be estimated based on difference(s) in ultrasonic signal propagation time (or difference in ultrasonic signal propagation speed) between signals propagating differently with respect to fluid flow. For instance, the difference in ultrasonic signal propagation speed in water between an upstream propagating signal and a downstream propagating signal is linearly proportional to the water flow rate at least for a practical range of water flow rates.

Fluid flow speed (or fluid flow rate) can be estimated based on relative time delays associated with signals propagating differently (e.g., upstream and downstream signal) with respect to fluid flow in the lumen. Such relative time delays can be, in some cases, in the range of nano-seconds (ns). In order to accurately measure (or estimate) the relative time delays between ultrasonic signals, a flow meter can employ multiple analog-to-digital converters (ADCs) with respective ADC clocks running at relative time delays with respect to each other. The flow meter can interleave samples provided by separate ADCs to achieve an effective sampling rate for measured ultrasonic signals high enough to allow measuring relatively small time delays (such as in the range of nano-seconds). Using multiple ADCs increases the cost of the flow meter and poses technical challenges such as power efficiency and addressing mismatch in voltage offset between different ADCs. A flow meter also can employ a single high speed ADC to improve signal resolution. However, high speed ADCs are more expensive and consume significantly more power than ADCs with lower sampling rates. Also, employing a high speed ADC may not be enough to reach a given desired signal resolution.

FIG. 1 shows a diagram illustrating a flow meter system 100 mounted on a pipe 10. The flow rate meter system 100 includes two ultrasonic transducers 110 a and 110 b (also referred to either individually or collectively as transducer(s) 110), two waveguides 120 a and 120 b (also referred to either individually or collectively as waveguide(s) 120), a control circuit 150 coupled to the ultrasonic transducers 110 and a transducer block 130 for fixing the ultrasonic transducers 110 to the pipe 10. The control circuit 150 can include a processor 151 and an analog-to-digital converter (ADC) 155.

As shown in FIG. 1, the ultrasonic transducers 110 can be mounted in a non-invasive manner. In such configuration, the ultrasonic transducers 110 or the waveguides 120 do not interfere with the fluid flow path within the pipe 10. The ultrasonic transducers 110 or the waveguides 120 can be mounted on the pipe 10 without cutting or grooving the pipe 10. In an invasive configuration, the transducers 110 can be placed within openings of the pipe wall 11. The waveguides 120 can be optional. As such, the transducers 110 can be mounted to be directly in contact with, or close proximity to, the pipe 10 without waveguides 120.

Each of the ultrasonic transducers 110 can be capable of transmitting and receiving ultrasonic signals. For instance, the ultrasonic transducer 110 a transmits the ultrasonic signal 101 a, which propagates through the waveguide 120 a into the pipe 10, reflects back from the pipe wall 11 towards the waveguide 120 b and is received at the ultrasonic transducer 110 b. The ultrasonic transducer 110 b transmits the ultrasonic signal 101 b, which propagates through the waveguide 120 b into the pipe 10, reflects back from the pipe wall 11 towards the waveguide 120 a and is received at the ultrasonic transducer 110 a. In the pipe 10, fluid is flowing according to direction 12. As such, the ultrasonic signal 101 a propagates upstream (i.e., having a motion component along the axis of the pipe 10 with a direction opposite to the fluid flow direction 12) within the pipe 10 and the ultrasonic signal 101 b propagates downstream (i.e., having a motion component along the axis of the pipe 10 with a direction similar to the fluid flow direction 12). Given the propagation direction of the ultrasonic signals 101 a and 101 b with respect to the fluid flow direction 12, the respective propagation times are affected differently by the fluid flow. For instance, the propagation time of the downstream ultrasonic signal 101 b is expected to be shorter than that of the downstream ultrasonic signal 101 a. Ultrasonic signals propagating through the fluid are also referred to herein as ultrasonic signal(s) 101.

In some implementations, the ultrasonic transducers 110 can transmit signals in one direction (e.g., downstream or upstream). The processor 151 can compare signal propagation time of a downstream or upstream ultrasonic signal to propagation time associated with a signal propagating in non-moving fluid to determine the effect of fluid flow on signal propagation through the fluid. Also, while FIG. 1 shows an illustrative configuration of mounting the transducers 110 on the pipe 10, other configurations are contemplated by the current disclosure. For instance, the transducers 110 can be mounted across one another on the pipe 10, at an angle with respect to the longitudinal axis of the pipe such that the ultrasonic signals 101 can propagate between the transducers 110 without necessarily bouncing off the pipe wall 11 (e.g., propagating in a straight line between the transducers 101).

In some implementations, the flow meter system 100 can include more than two ultrasonic transducers 110. Each ultrasonic transducer 110 in the flow meter system 100 can be capable of acting as a transmitter and a receiver. Some ultrasonic transducers 110 in the flow meter system 100 can be configured (or designated) to act as transmitters while others can be configured (or designated) to act as receivers. While the system 100 employs the ultrasonic transducers 110 to transmit or receive signals, other types of signal transmitters/receivers such as acoustic or electromagnetic transmitters/receivers can be employed.

The ADC 155 can be configured to sample receive (RX) ultrasonic signals received at the ultrasonic transducers 110. The flow meter system 100 includes a single ADC converter 155. The sampling rate of the ADC 155 can be smaller than a sampling rate associated with a desired signal resolution (or desired sampling rate) for achieving accurate estimation of fluid flow rate, fluid flow speed, or relative time delays associated with received (RX) ultrasonic signals. For instance, the sampling period of the ADC 155 can be in the range of micro-seconds (μs) while a desired resolution of relative time delays between ultrasonic signals 101 propagating within the fluid can be in the range of nano-seconds (ns). In particular, accurate estimation of fluid flow rate (or fluid flow speed) may involve detecting time delays (e.g., between upstream and downstream signals) in the range of nano-seconds.

The ADC 155 can be coupled to the processor 151 or a memory associated with the control circuit 150. For instance, the ADC 155 can provide signal samples directly to the processor 151 or store the samples in a memory accessible by the processor 151. The control circuit 150 can further include a digital-to-analog converter (DAC) configured to convert waveform samples into analog signals. For instance, the DAC can convert samples of a digital excitation signal into a respective analog excitation signal that is provided as input to the ultrasonic transducer(s) 110. The processor 151 or a memory associated with the control circuit 150 can store the samples of the digital excitation signal. The ADC 151 can be capable of operating as an ADC and a DAC. The digital excitation signal can include a pseudo random noise, a pulse train with a given frequency, pure tone at a given frequency, liner or logarithmic chirp signal or frequency modulated pulse train (e.g., with increasing or decreasing frequency). In response to the input analog excitation signal, the transducer 110 can output a band-pass signal that is transmitted into the pipe 10.

The processor 151 can be configured to control the operation and timing of the ultrasonic transducers 110 (e.g., initiate transmission/reception of ultrasonic signals 101), control the operation of the ADC 155 (e.g., initiate signal sampling by the ADC 155), control the operation of one or more other components of the control circuit 150, initiate and mange communication with other devices, execute processes for estimating relative time delays between distinct signals or estimating fluid flow rate, managing power consumption of the flow meter system 100 or a combination thereof. The processor 151 can include one or more of a microprocessor, microcontroller, digital signal processor (DSP), and application-specific integrated circuit (ASIC). The control circuit 150 can also include communication circuit(s) or component(s) for communicating with other devices, one or more signal amplifiers, or other analog or digital circuitry.

FIG. 2 is a flow diagram illustrating a method 200 for estimating fluid flow rate or fluid flow velocity. Referring to FIGS. 1 and 2, the method 200 can include the ultrasonic transducers 110 transmitting one or more TX signals (stage 210) and receiving one or more respective RX signals (stage 220). The method 200 can include the ADC 155 sampling the one or more RX signals according to a first sampling rate (stage 230), and the processor 151 generating at least one high resolution RX signal based on samples of the one or more RX signals provided by the ADC 155 (stage 240). The at least one high resolution RX signal corresponds to a second sampling rate higher than the first sampling rate. The method 200 can also include the processor 151 computing, for each of the at least one high resolution RX signals, a respective cross-correlation signal between that high resolution RX signal and a waveform (stage 250). The method 200 can also include the processor 151 estimating fluid flow rate (or fluid flow speed) based on the computed cross-correlation signal(s) (stage 256).

The method 200 can include the transducers 110 transmitting one or more TX signals (stage 210) and receiving one or more respective RX signals (stage 220). The ultrasonic transducers 110 can transmit (such as responsive to instruction(s) or excitation signal(s) from the processor 151) one or more downstream signals, one or more upstream signals, or a combination thereof. The ultrasonic transducers 110 can transmit a plurality of copies or versions of a TX signal and receive a plurality of respective RX signals over a given time period. The plurality of copies or versions of the TX signal can include signals transmitted upstream, signals transmitted downstream, or a combination thereof. The given time period can be in the range of hundreds of micro seconds (μs), milli-seconds (ms) or any other time period during which channel characteristics are not expected to vary. The media (e.g., the pipe 10, the fluid, the waveguides, or a combination thereof) through which the ultrasonic signals propagate from one transducer to another can be viewed as a communication channel whose characteristics may vary, for instance, due to temperature variation of the media. The redundancy associated with the plurality of received RX signals corresponding to the plurality of transmitted copies or versions of the TX signal allows for noise reduction, for instance, by using averaging methods when estimating relative signal time delays (or differences between signal propagation times). The ultrasonic transducers 110 can transmit a plurality of copies of the TX signal that are synchronized with respect to the ADC clock signal. For instance, all the copies of the TX signal can have the same fractional (or differential) time delay (i.e., amount of delay modulo the ADC sampling period T) with respect to the ADC clock signal. In some implementations, the ultrasonic transducers 110 can transmit a plurality of versions of the TX signal having distinct fractional (or differential) time delays (i.e., amount of delay modulo the ADC sampling period T) with respect the ADC clock signal. The processor 151 can provide the same excitation signal as input to the transducer 110 to generate synchronized copies of the same TX signal or provide delayed versions (such as with distinct time delays) of an excitation signal as input to the transducer 110 to generate delayed versions of the same TX signal.

FIG. 3 is a diagram illustrating different implementations of copies or versions of a transmit (TX) signal for transmission within a given time period. According to a first scenario, the transducer 110 can transmit consecutively three (or any other number of) copies 301 a, 301 b and 301 c of the TX signal having the same fractional (or differential) time delay (e.g., zero fractional time delay) with respect to the rising edges of the ADC clock signal 310. As such, the relative transmission time delay between any two of the three copies 301 a, 301 b and 301 c of the TX signal can be a multiple of the period T (such as k×T where k is an integer) of the ADC clock signal 310.

According to a second scenario, the transducer 110 can transmit three (or any other number of) versions 302 a, 302 b and 302 c of the TX signal having distinct deterministic fractional (or differential) time delays with respect to rising edges of the ADC clock signal 310. For instance, the fractional time delays can be 0,

$\frac{T}{3}\mspace{14mu}{and}\mspace{14mu}\frac{2T}{3}$ resulting in linear tractional (or differential) time delays. If N (N is an integer) versions of the TX signal are transmitted over the given period of time, the corresponding fractional time delays with respect to the rising edges of the ADC clock signal 310 can be equal to 0,

$\frac{T}{N},\frac{2T}{N},\ldots\mspace{14mu},{\frac{\left( {N - 1} \right)T}{N}.}$ As will be discussed below, the processor 151 can employ knowledge of the deterministic fractional (or differential) time delays for the transmitted versions (e.g., versions 302 a, 302 b and 302 c) of the TX signal and the corresponding received RX signals to generate the high resolution RX signal. The transmitted versions 302 a, 302 b and 302 c of the TX signal can propagate through the fluid (between the transducers 110) over non-overlapping time intervals. For instance, the transmit times associated with the transmitted versions (e.g., versions 301 a, 302 b and 302 c) of the TX signal can be equal to t,

${t + \frac{T}{N} + {kT}},{t + \frac{2T}{N} + {2{kT}}},\ldots\mspace{14mu},{t + \frac{\left( {N - 1} \right)T}{N} + {\left( {n - 1} \right){{kT}.}}}$ Even though the transmitted versions of the TX signal are non-overlapping in time, the fractional (or differential) time delays 0,

$\frac{T}{N},\frac{2T}{N},\ldots\mspace{14mu},\frac{\left( {N - 1} \right)T}{N}$ are uniformly spaced apart from each other within the ADC clock signal period T (or ADC sampling period). In some implementations, the fractional (or differential) time delays can be non-uniformly spaced within the period T.

According to a third scenario, the transducer(s) 110 can transmit three (or any other number of) versions 303 a, 303 b and 303 c of the TX signal with distinct respective random time delays (e.g., uttering delays) α₁, α₂ and α₃ with respect to rising edges of the ADC clock signal 310. The processor 151 can generate the values for α₁, α₂ and α₃ as instances of a random variable (such as a uniform random variable, Gaussian random variable, Ki-squared random variable or other random variable). In general, the processor 151 can generate N jitter time delays α₁, α₂, α_(N) as N instances of a random variable for N respective versions of the TX signal to be transmitted within the given time period. In some implementations, applying jitter delays to the transmission times of the versions of the TX signal helps mitigate errors, such as errors due to finite precision computing, in respective measured (or estimated) propagation times.

FIGS. 4A-4C show simulation results illustrating behavior of differential propagation times between downstream and upstream TX signals in a zero-flow fluid with and without jitter delays. The y-axis in FIGS. 4A-4C represents the differential propagation time between downstream and upstream signals and the x-axis represents the average propagation time for downstream and upstream signals. The differential propagation time is the measured time difference between downstream propagation time and upstream propagation time for a respective pair of transmitted signals including a downstream and upstream signals.

FIG. 4A shows simulation results for downstream and upstream signals with no jitter delays applied. FIG. 4B shows simulation results for downstream and upstream signals with jitter delays between 0 and 25 ns applied. FIG. 4C shows simulation results for downstream and upstream signals with jitter delays between 0 and 250 ns applied. For all simulation results in FIGS. 4A-4C, the downstream and upstream propagation times are associated with non-moving fluid (i.e., with flow rate equals 0 gallons per minute (GPM)). In zero-flow (i.e., still fluid) condition, one would expect recorded differential propagation times to be equal to zero. However, due to signal noise and computational errors, the recorded differential propagation times may not be exactly zero. By comparing the results in FIGS. 4A-4C, one can see that when no jitter delays are applied to the transmission times (as shown in FIG. 4A), the recorded differential propagation times exhibit relatively (e.g., compared to results in FIGS. 4B and 4C) larger deviations from zero. Also, as the average signal propagation time increases (i.e., increase along x-axis), the recorded differential propagation times exhibit a cumulative oscillation behavior around zero. However, when jitter delays are applied (as shown in FIGS. 4B and 4C), the recorded differential propagation times become closer to zero implying smaller respective errors. Also, while the results shown in FIG. 4B still show relatively larger errors and a cumulative oscillation behavior around zero as the average signal propagation time increases, the results shown in FIG. 4C illustrate an even smaller error with no oscillation behavior. As illustrated through the simulation results shown in FIGS. 4A-4C, the jitter delays applied to the transmission times of the transmitted versions of the TX signal mitigate the errors in the measured differential propagation times between downstream and upstream signals, and therefore allow for more accurate estimation of the propagation times and the differential propagation times of the transmitted versions of the TX signal.

Referring again to FIG. 3, according to a fourth scenario, the transducer(s) 110 can transmit three (or any other number of) versions 304 a, 304 b and 304 c of the TX signal with respective time delays (with respect to rising edges of the ADC clock signal 310) defined as accumulations of deterministic and jitter delays. For instance, the fractional time delays associated with the versions 304 a, 304 b and 304 c of the TX signal (with respect to rising edges of the ADC clock signal 310) can be equal to α₁,

${{\alpha_{2} + {\frac{T}{N}\mspace{14mu}{and}\mspace{14mu}\alpha_{3}}} = \frac{2T}{N}},$ respectively. For N transmitted versions of the TX signal, the respective fractional time delays can be equal to α₁,

${\alpha_{2}\; + \frac{T}{N}},{\alpha_{3} + \frac{2T}{N}},\ldots\mspace{14mu},{\alpha_{N} + {\frac{\left( {N - 1} \right)T}{N}.}}$ As such, each fractional time delay associated with a respective transmitted version of the TX signal is an aggregation of a deterministic time delay value

$\left( {{e.g.},\frac{nT}{N},} \right.$ where n is an integer between 0 and N−1) and a jitter time delay value (e.g., α_(i) where i is an index between 1 and N).

In some implementations, the processor 151 can apply the above described time delays to an excitation signal provided as input to the transducer(s) 110, and in response, the transducer(s) 110 can generate corresponding TX signals with the same time delays applied to the corresponding excitation signal. While the scenarios shown in FIG. 3 are described with respect to time delays, the same scenarios can be implemented by applying phase shifts in the frequency domain. That is, instead of applying time delays to the excitation signals, the processor 151 can add phase shifts to the versions of the excitation signal in the frequency domain. The phase shifts can be deterministic phase shifts (i.e., corresponding to the second scenario), jitter phase shifts (corresponding to the third scenario) or a combination thereof (corresponding to the fourth scenario). The processor 151 can use fast Fourier transform (FFT) to transform the excitation signal to the frequency domain and inverse fast Fourier transform (IFFT) to transform phase-shifted versions of the excitation signal back to the time domain. In some implementations, the control circuit 150 can store a copy of the excitation signal and/or copies of the respective phase-shifted versions in the frequency domain in order to avoid repetitive FFT and/or IFFT computations. While the fractional time delays described above with respect to FIG. 3 are defined with respect to rising edges of the ADC clock signal 310, such fractional time delays can be defined with respect down edges or other references associated with the ADC clock signal 310.

The method 200 can include the ADC 155 sampling each of the received RX signals at a first sampling rate R₁ (stage 230). For instance, the sampling rate R1 can be associated with a sampling period equal to ADC clock period T or a multiple thereof. The ADC 155 can be coupled to the ultrasonic transducers 110 and configured to receive the RX signals directly from the transducers 110. In some implementations, an amplifier can amplify the received RX signals before the sampling process. Upon sampling the received RX signals, the ADC 155 can provide the respective samples to the processor 151 or a memory accessible by the processor 151. In some implementations, the first sampling rate R₁ can be smaller than a desired fine signal resolution (or a desired second sampling rate R_(d)). For instance, the first sampling rate can be in the range of hundreds of Mega Hertz (MHz) whereas the desired fine signal resolution can be associated with a second sampling rate in the range of Giga Hertz (GHz).

Referring back to FIG. 2, the method 200 can include the processor 151 generating, based on the samples of received RX signals, at least one respective fine resolution RX signal associated with a second sampling rate R_(d) higher than the first sampling rate R₁. Given the first and desired sampling rates R₁ and R_(d), the processor 151 can determine resolution factor rf

$\left( {{{such}\mspace{14mu}{as}\mspace{14mu}{rf}} = {\left\lfloor \frac{R_{d}}{R_{1}} \right\rfloor\mspace{14mu}{or}\mspace{14mu}\left\lfloor \frac{R_{d}}{R_{1}} \right\rfloor}} \right).$ The processor 151 can then generate the fine resolution RX signal(s) based on the resolution factor rf and samples of the received RX signal(s).

FIG. 5 is a diagram illustrating a process of interleaving samples from multiple received RX signals to generate a respective higher resolution interleaved signal. For instance, the ultrasonic transducers 110 can transmit multiple copies of the TX signal with linear (or non-linear) incremental fractional time delays with respect to the ADC clock signal (for instance, as discussed with respect to the second scenario of FIG. 3). In the example shown in FIG. 5, a first transducer 110 can transmit two versions of the TX signal with fractional time delays equal to 0 and

$\frac{T}{2},$ respectively. A second transducer 110 can receive the respective RX signals and an amplifier associated with the control circuit 150 can amplify the received RX signals. The ADC 155 can then sample the amplified RX signals at a first sampling rate (e.g., equal to 4 MHz). The samples of the first RX signal 501 a and the samples of the second RX signal 501 b are out-of-sync by

$\frac{T}{2}.$ The processor 151 can interleave the samples of the first and second RX signals 501 a and 501 b to generate a respective higher resolution interleaved resolution RX signal 502 with a respective effective sampling rate equal to (e.g., 8 MHz) twice the first sampling rate of the ADC 155. While the example illustrated in FIG. 5 shows interleaving of samples from two distinct RX signals (such as RX signals 501 a and 501 b), any number of RX signals can be employed to generate the interleaved signal 502.

In some implementations, the processor 151 can cause the first transducer 110 to transmit a number of versions of the TX signal equal to the resolution factor rf with respective incremental fractional time delays (or corresponding incremental phase shifts). The processor 151 can then interleave the samples of the respective rf received RX signals to generate a fine resolution RX signal with a second sampling rate R₂=rf·R₁. The incremental time delays can be incremental deterministic time delays (as discussed with respect to the second scenario of FIG. 3) or a combination of incremental deterministic time delays and jitter time delays (as discussed with respect to the fourth scenario of FIG. 3).

FIG. 6 is a diagram illustrating a process of up-sampling a digital signal associated with one or more ADC-sampled RX signals to generate a respective higher resolution up-sampled RX signal. The input digital signal 601 to be up-sampled can be a single ADC-sampled RX signal an interleaved signal generated by interleaving samples from multiple received RX signals (for instance as discussed above with regard to FIG. 5). The processor 151 can insert zeros into an input digital signal 601 (block 610). For instance, if the input digital signal 601 is a sampled RX signal, for each sample of the sampled RX signal, the processor 151 can insert rf-1 zeros (such as preceding or following the original sample). The processor 151 can then interpolate the samples of the zero-padded signal using a low pass filter or a transfer function thereof (block 620) to generate the fine resolution signal 602. In some implementations, the transfer function of the low-pass filter 605 can be a truncated sinc function. For instance, the transfer function 605 can be a truncated sinc function including a single lobe (i.e., the main lobe of the sinc function), truncated sinc function including three lobes or other truncation of the sinc function. In some implementations, the zero-padding at block 610 and the interpolation at block 620 can be implemented as a single filtering operation. In some implementations, other functions (such as a triangular function, or a truncated Gaussian function) can be employed for interpolation. In some implementations, the processor 151 can insert, for each signal sample of the input digital signal 601, rf-1 copies of that sample instead of employing zero padding.

FIG. 7 shows experimental results for measured differential propagation times using up-sampled RX signals. The experimental results are generated based on a ¾ inch CPVC (Chlorinated Polyvinyl Chloride) pipe, 1 MHz ultrasonic transducers and 4 MHz ADC. The experimental results shown in plots (a)-(c) include 200 differences in propagation times (between downstream and upstream signals) measured for various flow rates. The continuous lines represent the average difference in propagation time (computed by averaging the measured differences in propagation time values at respective fluid flow rates) as a function of the fluid flow rate. The difference in propagation time values are measured by cross-correlating the up-sampled RX signals with a reference waveform having a respective sampling rate of 4 MHz.

With respect to the experimental results shown in plot (a), the received RX signals are zero-padded to achieve an up-sampling rate of 256 but no interpolation is applied when generating the respective up-sampled (or fine resolution) RX signals. The corresponding mean-square error (MSE) for the average difference in propagation times shown in the plot (a) is 0.006. With respect to the experimental results shown in plot (b), the RX signals are zero-padded and an interpolation based on a zero-order-hold filter is then applied to the zero-padded signal to achieve an up-sampling rate of 256. The corresponding MSE is 0.0009975. With respect to the experimental results shown in plot set (c), the received RX signals are zero-padded and an interpolation based on a truncated sinc function with a single lobe is then applied to the zero-padded signal to achieve an up-sampling rate of 256. The corresponding MSE is 0.0001623. The computed MSEs illustrate that more accurate estimations of the differential propagation times can be achieved when using the truncated sinc function (e.g., with 512 samples) for interpolation compared to the case where no interpolation is applied (plot (a)) or an interpolation using a zero-order-hold filter is applied (plot (b)). That is, employing the truncated sinc function (e.g., truncated to include a single lobe) for interpolation allows for substantial improvement in terms of the accuracy of the estimated (or measured) signal propagation times. Also, truncating the sinc function (or any other transfer function of a respective low-pass filter) allows of reduction in computational complexity.

Referring back to FIGS. 2, 5 and 6, the processor 151 can generate the fine resolution signal by employing both signal interleaving (as discussed with regard to FIG. 5) and up-sampling (as discussed with regard to FIG. 6). Signal interleaving allows for accurately increasing signal resolution using RX signals received over a timer period during which channel characteristics do not vary (or at least do not vary significantly). However, in some instances, such time period may not be sufficient to transmit rf non-time-overlapping TX signals (and in response receive rf corresponding RX signals). For instance, if the time period during which channel characteristics are substantially non-varying is 5 ms and the time duration for transmitting each signal is 0.1 ms, the flow meter system can use at most 50 RX signals for interleaving to achieve an interleaved signal with effective sampling rate equal to 50 times the sampling rate of the RX signals. If the resolution factor rf is larger than 50 (such as rf=256), the flow meter system 100 can further apply up-sampling (as discusses with regard to FIG. 6) to an interleaved signal to generate a fine resolution RX signal with the desired resolution R_(d). Also, in some instances, the ADC sampling rate may be smaller than the Nyquist rate. In such instances, signal interleaving can be employed to avoid aliasing. The interleaved signal(s) can then be up-sampled to generate the fine resolution signal with desired resolution R_(d).

Referring back to FIG. 2, the method 200 can include computing a cross correlation signal between the fine resolution RX signal and a reference waveform (stage 250) and determining a difference in propagation time between the reference waveform and the fine resolution RX signal. The reference waveform can be a representation (e.g., a sampled version) of an upstream RX signal, downstream RX signal, zero-flow RX signal (i.e., a RX signal received when the fluid flow rate is zero), TX signal, or a waveform derived therefrom. For instance, if the fine resolution RX signal is generated based on one or more downstream RX signals, the reference waveform can be an upstream RX signal or a zero-flow RX signal. If the fine resolution RX signal 502 or 602 is generated based on one or more upstream RX signals, the reference waveform can be associated with a downstream RX signal, a zero-flow RX signal or the respective TX signal. In some instances, the processor 151 can produce the reference waveform by filtering the TX signal (or the respective excitation signal) using a filter configured to model signal distortions induced by the transducers 110, the pipe 10, the fluid, the amplifier (if any), the ADC 155, the waveguides 120, or a combination thereof.

In some implementations, the reference waveform can be a sine wave or other narrowband signal. In such implementations, the processor 151 can compute a first cross correlation signal representing cross correlation between an upstream RX signal and the sine wave (or the narrowband signal), and a second cross correlation signal representing cross correlation between a downstream RX signal and the sine wave (or the narrowband signal). Using the first and second cross correlation signals, the processor 151 can determine a difference in signal propagation time between the upstream signal and the downstream signal. The processor 151 can determine such difference in signal propagation time based on a time shift between the first and second cross correlation signals. For instance, the processor can determine the time shift as the time shift between two local maxima (or two local minima or two zero crossings) associated with the first and second cross correlation signals, respectively. In some instances, the first and second cross correlation signals can be associated with an upstream RX signal and a zero-flow signal (or a zero-flow signal and a downstream signal).

In some implementations, the processor 151 can filter two RX signals (such as an upstream and a downstream RX signals, a zero-flow and an upstream signals, or a downstream and a zero-flow RX signals) using a narrowband filter and then compute a cross correlation signal between the filtered signals. In such implementations, one of the filtered RX signals acts as the reference waveform. Applying band-pass filtering, or using a narrowband signal (such as a sine waveform) as the reference waveform, allows for estimating the difference in signal propagation time with respect to narrow components of the RX signal(s). Such approach provides better accuracy, especially if the ultrasonic signal speed in the fluid (or across the pipe wall 11) varies in terms of frequency. Using narrowband components of received RX signals allows for mitigation of any errors, in estimating the difference in signal propagation time, due to signal speed variation as a function of signal frequency.

The reference waveform can have a respective resolution corresponding to the first sampling rate, the second sampling rate or a sampling rate in between. Computing a full cross-correlation signal (e.g., including all cross correlation values based on the samples of the fine resolution signal and the reference waveform) is computationally demanding as it involves a huge number of multiplications. FIGS. 8A-D illustrate processes for estimating time shifts between distinct signals based on efficient computations of cross correlation values.

FIG. 8A shows a block diagram illustrating a process 800 of estimating a time shift between a reference waveform and a fine resolution RX signal based on partial cross-correlation signal(s). The processor 151 can be configured to compute a cross-correlation signal based on an input signal 801 generated based on one or more RX signals and a first reference waveform 805. The input signal 801 can be a received RX signal (downstream or upstream), up-sampled version of a received RX signal, interleaved version of two or more received RX signals, a narrowband filtered version of a RX signal, or other signal representative of one or more RX signals. The fine resolution signal 802 can represent a fine resolution version of the input signal 802, a fine resolution version of one or more RX signals, or a fine resolution version of one or more narrowband filtered RX signals. The effective sampling rate of the input signal 801 can be a rate ranging between R₁ to R_(d).

The second reference waveform 807 can be a sampled zero-flow RX signal (or a narrowband filtered version thereof), a sampled upstream RX signal (or a narrowband filtered version thereof), a sampled downstream RX signal (or a narrowband filtered version thereof), an interleaved and/or up-sampled version of a RX signal (or a narrowband filtered version thereof), a sine wave, or a narrowband signal, while the first reference waveform 805 can be a truncated, down-sampled or trimmed version of a the second reference waveform 807. For instance, the first reference waveform 805 can be produced by nullifying (e.g., forcing to be zero) the samples of the second reference waveform 807 with respective amplitudes that are smaller than a given threshold value. Such threshold value can be equal to 90%, 95% or other percentage of the peak sample value of the second reference waveform 807. In some implementations, the first reference waveform 805 can be defined as a portion of the second reference waveform 807 associated with a respective time window. For instance, samples of the first reference waveform 805 can be equal to respective samples of the second reference waveform 807 within the given time window and equal to zero outside the given time window. The time window can be selected (or defined) to capture the high energy samples (such as around the peak value) of the second reference waveform 807. The first and second reference waveforms 805 and 807 can be generated during calibration of the flow meter system 100. The first and second reference waveforms 805 and 807 can be generated on the fly based on one or more received RX signals. In some instances, the fine resolution signal 802 can be representative of one or more down-stream RX signals and the first and second waveforms 805 and 807 can be generated based on one or more upstream RX signals (or vice versa). Using truncated, down-sampled, or trimmed version of a received RX signal (or of a signal representative of one or more RX signals) allows for reduction in computational complexity when computing the first cross-correlation signal.

The processor 151 can then determine a first estimate of the difference in signal propagation time associated with two distinct RX signals based on the computed first cross-correlation signal (block 810). For example, if the first reference waveform 805 is a representation of a RX signal, the processor 151 can compute the first estimate of the difference in signal propagation time as the time shift between the first reference waveform 805 and the input signal 801 based on the correlation signal computed using the first reference waveform 805 and the input signal 801. However, if the first reference waveform 805 is a sine wave or a narrowband signal, the processor 151 can compute a cross correlation signal using a first input signal 801 (e.g., representing a downstream RX signal) and the first reference waveform 805, and another cross correlation signal using a second input signal 801 (e.g., representing an upstream RX signal) and the first reference waveform 805. The processor can then determine a first estimate of the difference in signal propagation time associated with the first and second input signals 801 as the time shift between the computed cross correlation signals. In some implementations, instead of computing a coarse estimate of the time shift between the input signal 801 and the first input reference waveform 805, the processor 151 can identify a reference point (e.g., a local or global maximum, a local or global minimum, or a zero crossing) associated with the based on the correlation signal computed using the first reference waveform 805 and the input signal 801.

The first estimate of the difference in signal propagation time (or the identified reference point(s)) can be used to determine an accurate estimate of the difference in signal propagation time between the fine resolution signal 802 and the second reference waveform 807 (or two fine resolution signals 802 associated with two input signals 801 where the second reference waveform 807 is a sine wave or a narrowband signal). The processor 151 can locate a global or local maximum, a global or local minimum, or a zero crossing of a first cross-correlation signal computed using the first reference waveform 805 and an input signal 801, as an initial guess to determine a more accurate position of a corresponding global or local maximum, a corresponding global or local minimum, or a corresponding zero crossing in a second cross-correlation signal computed using the second reference waveform 807 and a high resolution signal 802. In order to determine an accurate estimate of the difference in signal propagation time between the fine resolution signal 802 and the second reference waveform 807 (or two fine resolution signals 802 where the second reference waveform 807 is a sine wave or a narrowband signal), the processor 151 can compute a second cross-correlation signal (e.g., a partial cross-correlation signal) using the fine resolution RX signal 802 and the second reference waveform 807. In computing the second cross-correlation signal, the processor 151 can compute respective samples associated with a neighborhood of a reference point in the second cross-correlation signal computed using the fine resolution RX signal(s) 802 and the second reference waveform 807. In other words, the processor 151 can compute a subset of the samples of the second cross correlation signal around the reference point. The reference point can be determined based on a corresponding reference point associated with the first cross-correlation signal computed using the input signal 801 and the first reference waveform 805.

FIG. 8B shows an illustration of the first and second cross correlation signals 830 and 840. The processor 151 can determine a first reference point 832 associated with (such as the peak of) the first cross-correlation signal 830 and use the first reference point 832 to determine a second reference point 842 (such as a local maximum) associated with the second cross-correlation signal 840. In some implementations, the processor 151 can employ an offset value 835 (e.g., determined during calibration of the flow meter system 100) to determine the second reference point 842 based on the first reference point 832. In some implementations, the processor 151 can then determine a time window 846 based on the second reference point 842 and can compute samples of the second cross-correlation signal 840 associated within that time window 846. The time window 846 can be centered at (or including) the second reference point 842. By using the time window 846, the processor 151 can compute a relatively small number of cross-correlation values when computing the second cross-correlation signal.

In order to determine an accurate estimate of the difference in signal propagation time, the processor 151 can then search for a local maximum (or other feature such as a local minimum or zero crossing) of the second cross-correlation signal 840 based on the time window 846 (block 820 of FIG. 8A). In some implementations, the time window 846 can be defined to include a single local maximum regardless of its location within the second cross-correlation signal 840. The processor 151 can determine the time shift between the fine resolution RX signal 802 and the second reference waveform 807 (or between two fine resolution signals 802 where the second reference waveform 807 is a sine wave or a narrowband signal) based on the determined local maximum (or other feature) of the second cross-correlation signal 840. For instance, if the local maximum value is the cross-correlation sample generated as Σr(n). f(n+τ) where r(n) is the second reference waveform 807 and f(n) is the fine resolution RX signal 802, then τ is the time delay between the fine resolution RX signal 802 and the second reference waveform 807. However, where the second reference waveform 807 is a sine wave or a narrowband signal, the processor 151 can determine the time shift between two fine resolution signals 802 as the time shift between corresponding local maxima (or local minima) in two cross correlation signals computed between the two fine resolution signals 802 and the second reference waveform 807. In some implementations, the processor 151 can be configured to slide the time window 846 (and repeat searching for the local maximum) if the respective local maximum (or other reference feature) is determined to be on a boundary of the time window 846.

FIG. 8C shows a cross-correlation plot and a state machine diagram illustrating a process for determining a cross-correlation feature value (such as local maximum or local minimum) associated with a respective time window 846. Given the time window 846, the processor 151 can compute all cross-correlation values within the time window 846. As discussed above with respect to FIG. 8B, the processor 151 can define the time window 846 based on a first reference point 832 associated with the first cross-correlation signal 830. The processor 151 can locate a feature value (such as local maximum or local minimum) within the time window 846. If the value is not on the boundary of the time window 846 (not at L or R), the processor 151 can stop the search process and use the determined location of the feature value to determine the time delay between the fine resolution RX signal 802 and the second reference waveform 807. If the location of the feature value is determined to be at the right boundary (at point R) of the time window 846, the processor 151 can shift the time window 846 to the right and restart the search process for the feature value. If the location of the feature value is determined to be at the left boundary (at point L) of the time window 815, the processor 151 can shift the time window 846 to the left and restart the search process. Shifting the time window 846 can include computing additional cross-correlation values (e.g., not previously computed). As shown in the state machine diagram, the processor 151 can stop the search process if the cross-correlation peak is determined to be located (i) not on a boundary point of the time window 846, (ii) on the right boundary point of the time window 846 after a left-shift or (iii) on the left boundary point of the time window after a right-shift.

FIG. 8D is a diagram illustrating a ternary search for locating a feature value (such as local maximum or local minimum) within a time window 846. The processor can be configured to segment the time window 846 into three overlapping time segments; a left segment 847, a center segment 848 and a right segment 848. In some implementations, the time window 846 can have a length equal to an up-sampling factor UF (or resolution factor rf) associated with the fine resolution RX signal 802. The processor 151 can compute and compare cross-correlation values at a middle point P and boundaries points L and R of the center segment 848.

If the cross-correlation value associated with the left boundary point L is determined to be the largest (among three computed values), the processor 151 can sub-divide the time left segment 847 into three respective overlapping sub-segments (similar to segmentation of time window 846). The processor 151 can then compare the cross-correlation values associated with the middle and boundary points of the middle sub-segment within the left segment 847 (similar to points L, P and R of segment 848). If the cross-correlation value associated with the right boundary point R is determined to be the largest (among three computed values), the processor 151 can sub-divide the right segment 849 into three respective overlapping sub-segments (similar to segmentation of time window 846). The processor can then compare the cross-correlation values associated with the middle and boundary points of the middle sub-segment within the right segment 849 (similar to points L, P and R of segment 848). If the cross-correlation value associated with the middle point P is determined to be the largest (among three computed values), the processor 151 can then segment the center segment 848 into three overlapping sub-segments and apply the same search process to the three sub-segment. That is, the processor 151 can compute cross correlation values associated with the middle and boundary points of the center sub-segment and compare such values to determine which segment is to be further sub-divided in smaller segments.

The processor 151 can repeat the process described above until the center sub-segment cannot be segmented any further, in which case the location of the largest cross-correlation value determined through the search process is checked. If the largest cross-correlation value (found by the ternary search process) is found to be smaller any of the cross-correlation values at the boundary points (such as at 0 or UF-1) of the original time window 846, the processor 151 can shift the time window 846 towards the boundary point (such as to the left or to the right) with the largest cross-correlation value and repeat the ternary search process for the shifted time window. If the largest cross-correlation value (determined by the ternary search process) is found to be greater than both cross-correlation values at the boundary points (such as at 0 or UF-1) of the original time window 846, the processor 151 can use the largest cross-correlation value determined by the ternary search process as the local maximum. In some implementations, the processor 151 can be configured to store cross-correlation values computed at each stage of the ternary search process to avoid repetitive computing of a given cross-correlation value.

The processes discussed with regard to FIGS. 8A-8D allow for computationally efficient estimation of the time delay between the fine resolution RX signal 802 and the second reference waveform 807. In particular, the discussed processes allow for significant reduction in the number of cross-correlation values computed even when fine resolution RX signals are employed. Also, the processor 151 can be configured to compute the first cross-correlation signal 830 only once. Once the respective first reference point 832 is determined, the processor 151 can use it for all subsequent fine resolution signals 802 to determine the time window 846. For instance, if the first reference point 832 is determined using an input signal 801 corresponding to a respective downstream RX signal, the processor 151 can use the same reference point (without re-computing the first cross-correlation signal 830) for subsequent downstream or up-stream RX signals to determine the respective time window 846.

In some implementations, the processor 151 can be configured to compute several estimates of the time delays between a plurality of received RX signals (e.g., including downstream and/or up-stream RX signals) and respective reference waveform(s) 807. When jitter delays are employed (as discussed with regard to FIG. 3), the processor 151 can be configured to take the added delay into consideration when determining the second reference point 842 based on the first reference point 832. The processor 151 can also be configured to average signal propagation times estimated based on two or more RX signals (e.g., associated with distinct jitter delays) to produce a final estimate of the signal propagation time.

Referring back to FIG. 2, the processor 151 can determine the fluid flow rate (or fluid flow speed) based on the determined time shift between the fine resolution RX signal 802 and the reference waveform or between two cross correlation signals associated with two fine resolution signals 802 (stage 260). The processor 151 can employ a lookup table or a formula to compute the fluid flow rate (or fluid flow speed). For instance, water flow rate is proportional to differential propagation time between downstream and upstream signals. The processor 151 can have access to a data structure (e.g., a lookup table) mapping time delays between RX signals and the reference waveform to corresponding fluid flow rates (or fluid flow speeds). In some implementations, the mapping can be dependent on the temperature of the fluid or the lumen. For instance, the fluid flow meter system 100 can include (or be couple to) a thermostat for measuring the temperature of the environment, the lumen or the fluid therein. In some implementations, the processor 151 can compute the fluid flow rate (or fluid flow velocity) based on a mathematical formula correlating differential propagation times to corresponding fluid flow rates (or fluid flow velocities).

FIG. 9 shows a block diagram illustrating another method for estimating fluid flow rate (or fluid flow velocity) based on recorded ultrasonic signals. The processor 151 can cross-correlate (block 910) a first RX signal (e.g., a downstream RX signal) 901 a with a reference waveform 907 that is generated based on a second RX signal (e.g., an upstream RX signal) 901 b. In some implementations, the first and second RX signals 901 a and 901 b are sampled at the first sampling rate (e.g., the sampling rate of the ADC 155). In some implementations, the processor 151 can produce the reference waveform 907 by applying a window operation to the second RX signal 910 b. That is, the reference waveform 907 represents a portion of the second RX signal 901 b that is associated with a time window 950. The processor 151 can then up-sample the cross-correlation computed based on the first RX signal 901 a and the reference waveform 907 by applying zero-padding (bock 920) followed by interpolation, for instance, using a truncated sinc function (block 93). The processor 151 can then locate the maximum of the cross-correlation signal to determine the relative time delay (or differential signal propagation time) between the first and second RX signals 901 a and 901 b. In some implementations, the processor 151 can apply a window search process (e.g., as discussed with regard to FIG. 8C) to locate the cross-correlation peak. In some implementations, the first RX signal 901 can be an upstream RX signal and the second RX signal can be a downstream signal. In some implementations, the first RX signal 901 a can be a downstream or upstream signal while the second RX signal can be zero flow RX signal.

Compared to the method described in FIG. 2, the method described in FIG. 9 does involve generating a fine resolution RX signal. The cross-correlation can be computed between signals sampled at the sampling rate of the ADC 155. However, the computed cross-correlation signal can be up-sampled to achieve better estimate of the relative time delay between the first and second RX signals 901 and 901 b.

While the systems, devices and methods in the current disclosure are described in terms of ultrasonic transducers, alternative flow rate sensors can include magnetic field sensors acoustic sensors or other sensors capable of sensing other types of signals propagating through a fluid in a lumen. The systems, devices and methods described in the current disclosure can be used to measure flow rates in fluid distribution systems such as water distribution systems, natural gas distribution systems, oil distribution systems, or other fluid distribution systems used in different industries.

While the invention has been particularly shown and described with reference to specific embodiments, it should be understood by those skilled in the art that various changes in form and detail may be made therein without departing from the spirit and scope of the invention as defined by the following claims. 

What is claimed is:
 1. A fluid flow meter system comprising: an analog-to-digital converter sampling a plurality of signals at a first sampling rate; and a processor configured to: generate a fine resolution signal using sampled versions of the signals converted by the analog-to-digital converter, the fine resolution signal having a second sampling rate higher than the first sampling rate; compute a cross-correlation signal indicative of cross-correlation between the fine resolution signal and a reference waveform; and determine an estimate of a fluid flow parameter of the fluid based on the computed cross-correlation signal.
 2. The fluid flow meter system of claim 1, wherein the fluid flow parameter includes fluid flow rate or fluid flow velocity.
 3. The fluid flow meter system of claim 1, wherein the plurality of signals are associated with two or more distinct jitter delays with respect to periods of the clock signal of the analog-to-digital converter.
 4. The fluid flow meter system of claim 3, wherein, in determining the estimate of the fluid flow parameter, the processor is configured to: determine a plurality of first estimates of the fluid flow parameter based on the plurality of signals associated with the two or more distinct jitter delays with respect to the periods of the clock signal of the analog-to-digital converter; and generate a final estimate of the fluid flow parameter by averaging the plurality of first estimates.
 5. The fluid flow meter system of claim 1, wherein generating a fine resolution signal includes up-sampling a signal associated with the sampled versions of the plurality of signals, the up-sampling includes applying interpolation using a truncated sinc function.
 6. The fluid flow meter system of claim 1, wherein the plurality of signals are associated with distinct incremental delays with respect to periods of the clock signal of the analog-to-digital converter.
 7. The fluid flow meter system of claim 6, wherein in generating the fine resolution signal, the processor is configured to interleave samples of the plurality of signals associated with distinct incremental delays with respect to the periods of the clock signal of the analog-to-digital converter.
 8. The fluid flow meter system of claim 7, wherein in generating the fine resolution signal, the processor is further configured to up-sample an interleaved signal generated by interleaving the samples of the plurality of signals associated with distinct incremental delays with respect to the periods of the clock signal of the analog-to-digital converter.
 9. The fluid flow meter system of claim 8, wherein in determining the time window, the processor is configured to: determine a first reference point associated with the first cross-correlation signal; determine a second reference point associated with the cross-correlation signal based on the first reference point; and determine the time window based on the second reference point.
 10. The fluid flow meter system of claim 9, wherein the processor is configured to nullify samples of the first reference waveform that are less than a threshold value.
 11. The fluid flow meter system of claim 9, wherein the signal associated with the sampled versions of the plurality of signals includes at least one of: a sampled version of a signal of the plurality of signals; an up-sampled version of a signal of the plurality of signals; an interleaved version of the sampled versions of the plurality of signals; and the fine resolution signal.
 12. The fluid flow meter system of claim 9, wherein the processor is further configured to: locate a maximum cross-correlation value of the plurality of cross-correlation values within the time window; in response to locating the maximum cross-correlation value at a boundary point of the time window, shift the time window towards that boundary point; and in response to locating the maximum cross-correlation value inside the time window, determine a time delay between the reference waveform and the fine resolution signal using a location of the maximum cross-correlation value inside the time window.
 13. The fluid flow meter system of claim 12, wherein in locating a maximum cross-correlation value inside the time window, the processor is configured to apply a ternary search process.
 14. The fluid flow meter system of claim 12, wherein the processor is configured to determine the estimated fluid flow parameter based on the time delay between the reference waveform and the fine resolution signal.
 15. The fluid flow meter system of claim 14, wherein the processor is configured to determine the estimated fluid flow parameter based on the time delay between the reference waveform and the fine resolution signal using a lookup table.
 16. The fluid flow meter system of claim 1, wherein the reference waveform represents a signal component associated with the plurality of signals.
 17. The fluid flow meter system of claim 1, wherein the reference waveform is associated with a zero-flow signal.
 18. The fluid flow meter system of claim 1, wherein in computing the cross-correlation signal, the processor is configured to: compute a first cross-correlation signal between a first reference waveform and a signal associated with the sampled versions of the plurality of signals, the first reference waveform different from the reference waveform and the first cross-correlation signal different from the cross-correlation signal; determine a time window based on the first cross-correlation signal; and compute the cross-correlation signal by computing a plurality of cross-correlation values within the time window and indicative of cross-correlations between the reference waveform and the fine resolution signal.
 19. The fluid flow meter system of claim 1, wherein the processor is configured to: in generating the fine resolution signal, generate a first fine resolution signal and a second fine resolution signal based on the plurality of signals, the first and second fine resolution signals associated with the second sampling rate; in computing the cross-correlation signal, compute a first cross-correlation signal indicative of cross-correlation between the first fine resolution signal and the reference waveform and compute a second cross-correlation signal indicative of cross-correlation between the second fine resolution signal and the reference waveform; and determine the estimate of the fluid flow parameter based on the first and second cross-correlation signals.
 20. The fluid flow meter system of claim 1, wherein the processor is configured to: generate the fine resolution signal as a filtered version of one or more corresponding signals using a bandpass filter; filter the reference waveform using the bandpass filter; and compute the cross-correlation signal using the fine resolution signal, generated as a filtered version of the one or more corresponding signals, and the filtered reference waveform. 